9780201795110

0201795116

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Summary

"Tom Pirnot" believes that conceptual understanding is the key to a student' s success in learning mathematics. He focuses on explaining the thinking behind the subject matter, so that students are able to truly understand the material and apply it to their lives. This textbook maintains a conversational tone throughout and focuses on motivating students and the mathematics through current applications. Ultimately, students who use this book will become more educated consumers of the vast amount of technical and mathematical information that they encounter daily, transforming them into mathematically aware citizens.

Table of Contents

Set Theory: Using Mathematics to Classify Objects

1

(67)

Problem Solving

2

(14)

Estimation

16

(7)

The Language of Sets

23

(7)

Comparing Sets

30

(8)

Set Operations

38

(12)

Survey Problems

50

(18)

Chapter Summary

58

(3)

Chapter Test

61

(2)

Of Further Interest: Infinite Sets

63

(5)

Logic: The Study of What's True or False or Somewhere in Between

68

(72)

Inductive and Deductive Reasoning

69

(9)

Statements, Connectives, and Quantifiers

78

(10)

Truth Tables

88

(12)

The Conditional and Biconditional

100

(10)

Verifying Arguments

110

(9)

Using Euler Diagrams to Verify Syllogisms

119

(21)

Chapter Summary

127

(2)

Chapter Test

129

(3)

Of Further Interest: Fuzzy Logic

132

(8)

Graph Theory: The Mathematics of Relationships

140

(54)

Graphs, Puzzles, and Map Coloring

141

(18)

The Traveling Salesperson Problem

159

(12)

Directed Graphs

171

(23)

Chapter Summary

180

(2)

Chapter Test

182

(2)

Of Further Interest: Scheduling Projects Using PERT

184

(10)

Numeration Systems: Does It Matter How We Name Numbers?

194

(50)

The Evolution of Numeration Systems

195

(11)

Place Value Systems

206

(11)

Calculating in Other Bases

217

(27)

Chapter Summary

230

(2)

Chapter Test

232

(1)

Of Further Interest: Modular Systems

233

(11)

Number Theory and the Real Number System: Understanding the Numbers All Around Us

244

(75)

Number Theory

245

(12)

The Integers

257

(9)

The Rational Numbers

266

(14)

The Real Number System

280

(12)

Exponents and Scientific Notation

292

(27)

Chapter Summary

303

(3)

Chapter Test

306

(1)

Of Further Interest: Sequences

307

(12)

Algebraic Models: How Do We Approximate Reality?

319

(65)

Linear Equations

320

(13)

Modeling with Linear Equations

333

(9)

Modeling with Quadratic Equations

342

(9)

Exponential Equations and Growth

351

(12)

Proportions and Variation

363

(21)

Chapter Summary

371

(3)

Chapter Test

374

(2)

Of Further Interest: Dynamical Systems

376

(8)

Modeling with Systems of Linear Equations and Inequalities: What's the Best Way to Do It?